Well, my approach to dealing with the additive versus sequential distinction was to add that other sense. Personally, I feel that if distinguishing those two is too much, then we cannot really justify all the other senses, which arguably bear a less important contrast. And if that is so... we might as well just reduce them all to a single sense.
As to the terminology, I am not sure if "additive relation" is immediately intuitive, but probably should be fine given that it is accompanied by a translation.
In any case, my input on how to word this can be found under my older proposal - just scroll down a bit and you will find an obscenely large change log under an edit by Mr. Breen, which was that proposal being reverted. Sadness, sadness.

Now; the reason why I made で a reading and the others not, is because it makes the entry and its notes shorter. 
て and で are the endings of all て forms; so - in theory - one should be able to identify all instances by those endings. Thence my note says "becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ" instead of "becomes いで after 五段 verbs ending in ぐ; becomes んで after 五段 verbs ending in ぬ、ぶ or む". 
Consider also that adding って means that we are missing んで, いで and いて in the readings and notes. Needless to say, the readings might be fine but such notes would end up covering a metric mile - which I am not necessarily against, but I am not the one you will need to convince anyway so...

Regarding your first point, I had that in mind, but I hadn't yet thought of a way to deal with that. I feel like having two senses may be a bit much. 
Perhaps having "indicates sequential or additive relation" works? That should be somewhat clear then with the glosses.
Or maybe "indicates simple conjunction or sequential relation"?

The "forming compound verbs" also checks out.

＞ I also have reverted the term 'subsidiary' to 'auxiliary' as I think the latter is more common and more likely to be immediately understood (plus, it is 1 letter shorter, which will surely make all the difference)
   ＞ I can live with that, it's indeed more common and easier to understand. I prefer to make the distinction (as do the references), but it's not typically done in JMdict AFAICS. 
      Then that xref can also go again

Regarding the attachment note, I agree it's probably better to leave it out here. It'd be more of a matter of formality rather than practicability.
＞ (maybe do something on the 音便形 page and cross reference it here?)
   ＞ I was thinking along these lines as well, but that'd most likely turn out as a very long and windy explanatory gloss.
      I believe this is fine

Since we are at 音便 already, this entry also needs to mention って, as in 知りて ＞ 知って, 立ちて ＞ 立って and 買ゐて＞買って.
I propose just adding that to the note. 

I have added って as a surface form

@@ -9,0 +10,3 @@
+<r_ele>
+<reb>って</reb>
+</r_ele>
@@ -13 +16 @@
-<s_inf>after the continuative form; indicates sequential relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>indicates sequential relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>
@@ -15 +18 @@
-<gloss>then</gloss>
+<gloss>(and) then</gloss>
@@ -20 +23 @@
-<s_inf>after the continuative form; indicates causal relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>indicates causal relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>
@@ -28 +31 @@
-<s_inf>after the continuative form; indicates instrumental relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>indicates instrumental relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>
@@ -35 +38 @@
-<s_inf>after the continuative form; indicates contrastive relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>indicates contrastive relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>
@@ -42,2 +45 @@
-<xref type="see" seq="1514640">補助動詞</xref>
-<s_inf>after the continuative form; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>
@@ -44,0 +47 @@
+<gloss>particle used to form compound verbs (as in やって来る)</gloss>
@@ -49 +52 @@
-<s_inf>at sentence end; indicates request or light imperative; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>at sentence end; indicates request or light imperative; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ; って after 五段 verbs ending in る, う or つ</s_inf>

Regarding [1]: The conjunction is not necessarily always sequential, it often its, and て has a tendency to chosen over the 連用形 if the relation between the conjuncts is sequential, but it is not restricted to those uses.
The most obvious case is with adjectives: 「黒くて高い」can be freely rephrased as 「高くて黒い」since no sequence is implied. This is why my older proposal had 7 senses as opposed to the current 6 - it had an extra one for the bare, non-sequential conjunction, which was [1].


Regarding compound verbs： I am referring to cases wherein verb + て + verb is analysed as just one verb. This use, like pretty much all others, is rooted in sense 1. Albeit rarer than the 連用形 compounds, it works under the same principles.
For example, 遣って来る, despite clearly being made from やる＋て＋くる、is given its own entry in Daijirin, Daijisen, Shinmeikai and Koujien. In all of these cases, it is listed as a カ変, rather than the expected 連語. There are more entries like this such as 取って代わる.
Perhaps an even better example is 打って変る, whose meaning is not really the sum of its parts.

Regarding the [conj] particle: As briefly mentioned above, pretty much all senses of て are rooted in its role as a conjunctive (which itself is rooted in its origin as the 連用形 of the ancient perfective auxiliary つ), with the exception being senses [5] and [6] of the current proposal wherein it cannot really be analysed as a conjunction - which is why I did not put in the tag and am thus removing it from [5]. 
I also have reverted the term 'subsidiary' to 'auxiliary' as I think the latter is more common and more likely to be immediately understood (plus, it is 1 letter shorter, which will surely make all the difference).

And lastly, stem connection: While the stem for the て form is regarded as being the 連用形 due to the etymological origins of the 音便形 as a sound change of the 連用形 + て, in practice the 音便形 is its own inflection.
As such, writing either 連用形, continuative form, or -masu stem, will not allow a reader to correctly deduce the inflection - instead they would end up producing an inflection right out of Old Japanese, such as 書きて instead of 書いて, etc. - this is why both foreign Japanese textbooks and native Japanese textbooks aimed at foreigners almost unanimously teach it as "て-form" or て形、 as an inflection itself.
I am not sure if there is a good way to convey that in this dictionary (maybe do something on the 音便形 page and cross reference it here?) as this is complicated by the fact that the "音便 stem" involves alteration of the verbal root.
I.e. Kak-, the root 書く, must lose the final k, receive the left-over -i from the 連用形, turn into Ka-i- and only then connect to て - which is unlike the other stems that are all simply concatenated onto the root: Kak-a/i/e/o/u.
Either way, I would drop that part of the note.

@@ -42 +41,0 @@
-<pos>&conj;</pos>
@@ -45 +44 @@
-<gloss>particle used to connect to subsidiary verbs (as in て-いる, て-いく, etc.)</gloss>
+<gloss>particle used to connect to auxiliary verbs (as in て-いる, て-いく, etc.)</gloss>

(See also Shinsen's entry for this, I can't add it here right now due to the issue described below)

Progressive 4：
－て

1〔事を終えて次に連続する意〕and
私は朝食を済ませて出掛けた
I had my breakfast and went out.／After finishing my breakfast, I went out.

2〔原因・理由を表す〕
重くて持ち上がらない
It's so heavy (that) I can't lift it.／It's too heavy for me to lift.
うれしくて飛び上がった
I jumped for joy.

3〔手段・方法を表す〕
フランス語を教えて生計を立てている
She earns her living by giving lessons in French.

4〔…のに〕
知っていて黙っていた
He knew about it, but he did not tell me.／Although he knew, he didn't tell me.

5〔軽い命令を表す〕
やめて
Stop it.

ーーーーーーーーーーーーーーーーーーーー

Firstly, I intended to submit my draft for this entry in this comment box at the bottom instead of outright changing all you have proposed (which I do agree with). 
However, when then attempting to submit that I get the error "The requested URL's length exceeds the capacity limit for this server.", which I haven't encountered so far.

ーーーーーーーーーーーーーーーーーーーー
＞ As I am editing this, [3] Is being shown as "[prt][col]" in the preview instead of "[prt,col]" despite having been formatted like the latter [...]
I reckon that is because they belong to different tag classes. [prt] belongs to the POS tags, while [col] is a misc tag.

＞ I fear that might lead a reader to believe that said note applies only to [1], which would be misleading.
I fear so too
ーーーーーーーーーーーーーーーーーーーー
Being a (relatively) new contributor to JMdict, I've never really looked at this entry, but I absolutely agree that the former version is very much insufficient. 
ーーーーーーーーーーーーーーーーーーーー
Also, I see that you've brought up the point about 接続助詞 below. The good news is that a [conj-prt] tag will most likely arrive in the near future, as I've raised that topic in the github issues.

Could you elaborate on sense 2 "particle used to form compound verbs"? I don't quite see that in references, since it's usually the bare 連用形 used for this purpose.

Stem attachment information tends to be included. However, adding the typical "after the -masu stem of a verb" doesn't suffice here. Perhaps "After the continuative form" is appropriate.
   連用形 and the likes are typically not used in sense notes in JMdict. Note that "continuative form" is searchable in JMdict and leads directly to the entry for 連用形.

The references I consulted (Shinsen, Sankoku, Daijirin) class the current sense 2 as "接続助詞" as well, so I added [conj] for now.

I see that the support has previously been lacking, but I believe that having separate senses for the different uses of the conjunctive aspect is necessary. 
   Compare shinsen above, which is quite neat, but not achievable in JMdict in that fashion.  
   I would argue that the entries for the most used "words" (items would be better), deserve the most care, i.e. specificity. And that does take time in some cases
ーーーーーーーーーーーーーーーーーーーー
Thus I propose something along the lines of this (subject to refinement)

@@ -13 +13 @@
-<s_inf>joins two sentences; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>after the continuative form; indicates sequential relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
@@ -14,0 +15 @@
+<gloss>then</gloss>
@@ -18,2 +19,27 @@
-<s_inf>becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
-<gloss>particle used to connect auxiliary verbs or to form compound verbs</gloss>
+<pos>&conj;</pos>
+<s_inf>after the continuative form; indicates causal relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>because (of)</gloss>
+<gloss>so</gloss>
+<gloss>since</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>after the continuative form; indicates instrumental relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>through (that)</gloss>
+<gloss>by</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>after the continuative form; indicates contrastive relation; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>although</gloss>
+<gloss>but</gloss>
+<gloss>(and) yet</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<xref type="see" seq="1514640">補助動詞</xref>
+<s_inf>after the continuative form; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>particle used to connect to subsidiary verbs (as in て-いる, て-いく, etc.)</gloss>
@@ -24 +50 @@
-<s_inf>at sentence end; used to make a request; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<s_inf>at sentence end; indicates request or light imperative; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>

Well, I did say that they were there to be picked out, and that only [1], [6] and [7] were strictly necessary. I still stand by what I said that this entry cannot stay like this, so, let us try that.
Repeating the note on で in every sense might be unneeded, maybe remove it from [2] and [3], leaving it only on [1]. However, I fear that might lead a reader to believe that said note applies only to [1], which would be misleading. Really wish we had notes that went over the entire glossary...

As I am editing this, [3] Is being shown as "[prt][col]" in the preview instead of "[prt,col]" despite having been formatted like the latter, hopefully it will actually be like that when I submit it, but if it does not, I do not know why it is like this.

@@ -6,0 +7,3 @@
+<r_ele>
+<reb>で</reb>
+</r_ele>
@@ -8,3 +11,15 @@
-<pos>&aux;</pos>
-<s_inf>で after certain verb forms</s_inf>
-<gloss>indicates continuing action</gloss>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>joins two sentences; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>and</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<s_inf>becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>particle used to connect auxiliary verbs or to form compound verbs</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<misc>&col;</misc>
+<s_inf>at sentence end; used to make a request; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>please (do)</gloss>

This long edit obviously is not getting any support. I'm switching it back to the predecessor, but leaving Non's suggestions visible. I found it to be far to detailed and complex to be a useful entry.

@@ -7,3 +6,0 @@
-<r_ele>
-<reb>で</reb>
-</r_ele>
@@ -11,39 +8,6 @@
-<pos>&prt;</pos>
-<pos>&conj;</pos>
-<s_inf>joins two sentences; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
-<gloss>and</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<pos>&conj;</pos>
-<s_inf>connects sentences in order of occurrence</s_inf>
-<gloss>and (then)</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<pos>&conj;</pos>
-<s_inf>connects sentences in causal relation</s_inf>
-<gloss>and (because of that)</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<pos>&conj;</pos>
-<s_inf>connects sentences in instrumental relation; preceding sentence is means by which following sentence takes place</s_inf>
-<gloss>and (through that)...</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<pos>&conj;</pos>
-<s_inf>forms contrastive conjunction</s_inf>
-<gloss>but...</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<xref type="see" seq="1577980">いる・3</xref>
-<gloss g_type="expl">used to connect to auxiliary verbs or to form compound verbs</gloss>
-</sense>
-<sense>
-<pos>&prt;</pos>
-<misc>&col;</misc>
-<s_inf>at sentence end</s_inf>
-<gloss g_type="expl">used to make a request</gloss>
+<pos>&aux;</pos>
+<xref type="see" seq="2028980">で・5</xref>
+<xref type="see" seq="2028980">で・5</xref>
+<xref type="see" seq="2028980">で・5</xref>
+<s_inf>で after certain verb forms</s_inf>
+<gloss>indicates continuing action</gloss>

I made somewhat of a revision of my proposal. As this has been drifting for months and nobody seems to want to touch it, I would like to highlight that I was not saying all these senses are needed, I made them in bulk so that an editor could pick them out if needed - the entry could be reduced to only [1], [6] and [7].

At any rate, I think the earlier versions of this unapproved entry should be closed, at least.

@@ -13,2 +13,2 @@
-<s_inf>forms plain conjunction; 1-7 become ～で after godan verbs ending in ぐ, む, ぶ or ぬ</s_inf>
-<gloss>and...</gloss>
+<s_inf>joins two sentences; becomes で after 五段 verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>and</gloss>
@@ -20 +20 @@
-<gloss>and then...</gloss>
+<gloss>and (then)</gloss>
@@ -26 +26 @@
-<gloss>and because of that...</gloss>
+<gloss>and (because of that)</gloss>
@@ -31,2 +31,2 @@
-<s_inf>connects sentences in instrumental relation</s_inf>
-<gloss>and through that... (preceding sentence is the means by which following sentence takes place)</gloss>
+<s_inf>connects sentences in instrumental relation; preceding sentence is means by which following sentence takes place</s_inf>
+<gloss>and (through that)...</gloss>
@@ -43 +43 @@
-<gloss g_type="expl">used to connect verbs to auxiliary verbs or to form compound verbs</gloss>
+<gloss g_type="expl">used to connect to auxiliary verbs or to form compound verbs</gloss>
@@ -48 +48 @@
-<s_inf>used at sentence end</s_inf>
+<s_inf>at sentence end</s_inf>

Proposing adding で to readings to go along with the proposal of deleting the sense of the cross-reference leading here.

@@ -5,0 +6,3 @@
+</r_ele>
+<r_ele>
+<reb>で</reb>

daijr, daijs

Changed [aux] to [prt] as it is classed as a 接続助詞. Completely changing glossary as "Indicates continuing action" will likely lead anyone learning of this word through this entry to think of a continuous verb rather than a conjunction.
Senses are based on the references listed, mainly daijr, they are not absolutely exhaustive but these should be the main ones. I opted to make [1] what it is as most other senses can be imposed upon it by context.

If accepted, I would like to suggest deleting the 5th sense of the entry on ～で that leads here: it is same word and the changes to notes in this entry should make it unnecessary.

@@ -8,4 +8,39 @@
-<pos>&aux;</pos>
-<xref type="see" seq="2028980">で・5</xref>
-<s_inf>で after certain verb forms</s_inf>
-<gloss>indicates continuing action</gloss>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>forms plain conjunction; 1-7 become ～で after godan verbs ending in ぐ, む, ぶ or ぬ</s_inf>
+<gloss>and...</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>connects sentences in order of occurrence</s_inf>
+<gloss>and then...</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>connects sentences in causal relation</s_inf>
+<gloss>and because of that...</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>connects sentences in instrumental relation</s_inf>
+<gloss>and through that... (preceding sentence is the means by which following sentence takes place)</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<pos>&conj;</pos>
+<s_inf>forms contrastive conjunction</s_inf>
+<gloss>but...</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<xref type="see" seq="1577980">いる・3</xref>
+<gloss g_type="expl">used to connect verbs to auxiliary verbs or to form compound verbs</gloss>
+</sense>
+<sense>
+<pos>&prt;</pos>
+<misc>&col;</misc>
+<s_inf>used at sentence end</s_inf>
+<gloss g_type="expl">used to make a request</gloss>

@@ -9,1 +9,1 @@
-<xref type="see" seq="2028980">で</xref>
+<xref type="see" seq="2028980">で・5</xref>

I wonder about the "aux". UniDic has "助詞,接続助詞" for this. I guess "aux" covers a multitude of sins.

@@ -9,0 +9,2 @@
+<xref type="see" seq="2028980">で</xref>
+<xref type="see" seq="2028980">で</xref>
@@ -10,1 +12,1 @@
-<gloss>used to indicate continuing action</gloss>
+<gloss>indicates continuing action</gloss>

actually, come to think of it, れる and られる could be merged with a note.  they're already sufficiently well-documented.

they have to be merged because one is merely an alternate pronunciation of the other that occurs with certain verb forms. れる and られる are clearly more divergent than て and で.

in addition, there is already an existing entry for で, and we try to avoid having entries with identical headword/reading combos.

@@ -7,3 +7,0 @@
-<r_ele>
-<reb>で</reb>
-</r_ele>
@@ -12,0 +9,1 @@
+<s_inf>で after certain verb forms</s_inf>

If these 2 needs to be merged as RENE suggested, I have no 
idea why れる・られる　or せる・させる are not merged.

All these require to follow complicated conjugation rule but 
the same word for each.

Criteria for an entity is a bit unclear.

@@ -6,0 +6,3 @@
+</r_ele>
+<r_ele>
+<reb>で</reb>

http://ja.wikipedia.org/wiki/助詞
http://ja.wiktionary.org/wiki/て

used with -masu stem verbs except for v5g, v5n, v5b, v5m